Prob & Stats 2.2

The​ ______ class limit is the smallest value within the class and the​ ______ class limit is the largest value within the class.

lower, upper

For heights of full-grown men in a country​,state whether you would expect a histogram of the data to be​ bell-shaped, uniform, skewed​ left, or skewed right

bell shaped

For ages of patients diagnosed with Alzheimer's disease in a hospital​, state whether you would expect a histogram of the data to be​ bell-shaped, uniform, skewed​ left, or skewed right.

skewed left

The following data represent the number of potholes on 35 randomly selected​ 1-mile stretches of highway around a particular city. Complete parts​ (a) through​ (d) to the right. (a) ​Construct a frequency distribution of the data. (b) ​Construct a relative frequency distribution of the data. (c) ​Using the results from part​ (b), what percentage of the stretches of highway have 3​ potholes? (d) ​Using the results from part​ (b), what percentage of the stretches of highway have 5 or more​ potholes?

(a) Potholes Frequency 1 10 2 6 3 7 4 4 5 4 6 2 7 2 (b) Potholes Rel Freq 1 0.286 2 0.171 3 0.2 4 0.114 5 0.114 6 0.057 7 0.057 (c) 20% (d) 22.8%

To predict future enrollment in a school​ district, fifty households within the district were​ sampled, and asked to disclose the number of children under the age of five living in the household. The results of the survey are presented in the table. Complete parts​ (a) through​ (c) below. # of kids <5 # of households 0 15 1 14 2 16 3 3 4 2 (a) Construct a relative frequency distribution of the data. (b) What percentage of households has two children under the age of 5? (c)​ What percentage of households has one or two children under the age of​ 5?

(a) # of kids <5 Relative Frequency 0 0.3 1 0.28 2 0.32 3 0.06 4 0.04 (b) 32 (c) 60

The following frequency histogram represents the IQ scores of a random sample of​ seventh-grade students. IQs are measured to the nearest whole number. The frequency of each class is labeled above each rectangle. Use the histogram to answers parts​ (a) through​ (g). (a) How many students were sampled? (b) Determine the class width (c) ​Identify the classes and their frequencies. Choose the correct answer below. (d) ​Which class has the highest​ frequency? (e) ​Which class has the lowest​ frequency? (f) What percent of students had an IQ of at least 120? (g) Did any students have an IQ of 163?

(a) 200 Students (b) The class width is 10 (c) 60-69, 2​;70-79, 4​; 80-89, 11​; 90-99, 40​; 100-109, 58​; 110-119, 40​; 120-129, 31; ​130-139, 9​; ​140-149, 4​;​150-159, 1 (d) 100-109 (e) 150-159 (f) 22.5 (g) ​No, because there are no​ bars, or​ frequencies, greater than an IQ of 160.

The data to the right represent the top speed​ (in kilometers per​ hour) of all the players​ (except goaltenders) in a certain soccer league. Find ​(a) the number of​ classes, ​(b) the class limits for the third ​class, and ​(c) the class width. Speed (km/hr) # of Players 10-14.9 5 15-19.9 14 20-24.9 35 25-29.9 35.3 30-34.9 169 (a) There are _____ classes (b) The lower class limit for the third class is __________ The upper class limit for the third class is ____ (c) The class width is ___________

(a) 5 (b) The lower class limit for the third class is 20 The upper class limit for the third class is 24.9 (c) 5

An Internet media and market research firm measured the amount of time an individual spends viewing a specific Webpage. The data in the accompanying table represent the amount of​ time, in​ seconds, a random sample of 40 surfers spent viewing a Webpage. Create the graphical summary. Write a sentence that describes the data. (a) Create a graphical summary. Choose the correct graph below. (b) Write a sentence that describes the data. Choose the correct answer below.

Chart A (b) The distribution is skewed right

______ are the categories by which data are grouped.

Classes

Why​ shouldn't classes overlap when summarizing continuous data in a frequency or relative frequency​ distribution?

Classes​ shouldn't overlap so there is no confusion as to which class an observation belongs.

What is the shape of the distribution​ shown?

Skewed right

Is the statement below true or false? There is not one particular frequency distribution that is​ correct, but there are frequency distributions that are less desirable than others.

The statement is true. Any correctly constructed frequency distribution is valid.​ However, some choices for the categories or classes give more information about the shape of the distribution.

For number of students per grade in a public school district​, state whether you would expect a histogram of the data to be​ bell-shaped, uniform, skewed​ left, or skewed right.

Uniform

An experiment was conducted in which two fair dice were thrown 100 times. The sum of the pips showing on the dice was then recorded. The frequency histogram to the right gives the results. Use the histogram to complete parts​ (a) through​ (f). (a) What was the most frequent outcome of the experiment? (b) What was the least frequent? (c) How many times did we observe a 7? (d) How many more 4's were observed than 12's? (e) Determine the percentage of time a 7 was observed. (f) ​Describe the shape of the distribution. Choose the correct answer below.

(a) 9 (b) 12 (c) 14 (d) 8 (e) 14 (f) skewed left

Chicago has installed cameras at various intersections throughout the city. The camera photographs the license plate of any car engaging in a moving violation​ (such as driving through a red light or failure to completely stop prior to turning on​ red). The given data set represents the number of violations recorded for a random sample of 60 cameras on October​ 17, 2018. Complete parts​ (a) through​ (d) below. (a) What type of data is "number of violations"? Choose the correct answer below. 0-4: 33 0.55 5-9: 16 0.26 10-14: 3 0.05 15-19: 1 0.01 20-24: 2 0.03 50-54: 1 0.01 (b) ​Draw a relative frequency histogram of the data using a lower class limit of the first class of 0 and a class width of 5. Describe the shape of the distribution. (c) Draw a dot plot below (d) Were there any cameras that did not record any violations on October 17, 2018? If so how many? Select the correct choice below and, if necessary, fill in the answer box within your choice.

(a) Discrete (b) C The shape of the distribution is Skewed right (c) B (d) ​Yes, there were cameras that did not record any violations on October​ 17, 2018. The number of cameras that did not record any violations is 2